An algorithm to compute a presentation of pushforward modules

TL;DR

This paper presents an improved algorithm for computing presentations of pushforward modules in finite map germs, with applications in singularity theory demonstrated through software implementation.

Contribution

It introduces an enhanced algorithm building on previous methods, enabling more efficient computation of pushforward modules for Cohen-Macaulay varieties.

Findings

Algorithm successfully computes pushforward modules

Implementation in Singular software demonstrates practical utility

Improves computational efficiency over prior methods

Abstract

We describe an algorithm to compute a presentation of the pushforward module $f_*{\mathcal O}_{\mathcal{X}}$ for a finite map germ $f\colon \mathcal{X}\to ({\mathbb{C}}^{n+1},0)$, where $\mathcal{X}$ is Cohen-Macaulay of dimension $n$. The algorithm is an improvement of a method by Mond and Pellikaan. We give applications to problems in singularity theory, computed by means of an implementation in the software Singular.